Preheat your oven to 400°F (200°C). Toss the diced butternut squash with 2 tablespoons of olive oil, salt, and pepper on a baking sheet. Spread it out in a single layer and roast for about 25 minutes, flipping halfway through until tender and slightly caramelized. Roasting brings out the natural sweetness and deepens the flavor.
While the squash is roasting, bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Reserve about 1 cup of pasta water before draining the pasta. This starchy water will help thin out the sauce if needed.
In a large skillet, heat the remaining tablespoon of olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant but not browned. Then add the chopped kale and cook, stirring often, until it wilts and turns bright green, about 3-4 minutes.
Pour the vegetable broth into the skillet with the kale, stirring to combine. Let it simmer for 2-3 minutes to infuse flavor and soften the greens. Add the roasted butternut squash to the pan and gently stir everything together.
Reduce heat to low and stir in the heavy cream, thyme, and red pepper flakes if using. Allow the sauce to heat through and slightly thicken, about 3-4 minutes. If the sauce seems too thick, add reserved pasta water a little at a time until you reach your desired consistency.
Add the cooked pasta to the skillet and toss everything together until the pasta is well coated in the creamy sauce with veggies. Taste and adjust seasoning with salt and pepper as needed. Serve immediately with fresh parsley or thyme sprinkled on top for a pop of color and freshness.